On the optimality of the ideal right-angled 24-cell

DOI10.2140/agt.2012.12.1941zbMath1272.52014arXiv1211.2944OpenAlexW3098347237MaRDI QIDQ691534

Alexander Kolpakov

Publication date: 3 December 2012

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.2944

zbMATH Keywords

hyperbolic manifoldright-angled Coxeter group24-cellCoexeter polytopevolume minimality

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) (n)-dimensional polytopes (52B11) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Polyhedra and polytopes; regular figures, division of spaces (51M20) Inequalities and extremum problems involving convexity in convex geometry (52A40) Spherical and hyperbolic convexity (52A55)

Related Items (8)

The number of cusps of right-angled polyhedra in hyperbolic spaces ⋮ Ideal right-angled polyhedra in Lobachevsky space ⋮ Hyperbolic four-manifolds with one cusp ⋮ Right-angled polyhedra and hyperbolic 3-manifolds ⋮ The growth rates of ideal Coxeter polyhedra in hyperbolic 3-space ⋮ New hyperbolic 4-manifolds of low volume ⋮ Horoball packings related to the 4-dimensional hyperbolic 24 cell honeycomb {3,4,3,4} ⋮ Infinitely many arithmetic hyperbolic rational homology 3–spheres that bound geometrically

Cites Work

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• The covolume of discrete subgroups of \(\mathrm{Iso}(\mathbb H^{2m})\)
• Geometry II: spaces of constant curvature. Transl. from the Russian by V. Minachin
• On right-angled reflection groups in hyperbolic spaces.
• Lectures on Polytopes
• The Volume Spectrum of Hyperbolic 4-Manifolds
• ON CONVEX POLYHEDRA IN LOBAČEVSKIĬ SPACES
• ON CONVEX POLYHEDRA OF FINITE VOLUME IN LOBAČEVSKIĬ SPACE
• Notes on right-angled Coxeter polyhedra in hyperbolic spaces.

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